STATISTICAL PROCESS CONTROL (SPC): A CONTROL TOOL
AGAINST WASTE OF INPUTS IN BRAZILIAN DAIRY
Tiago Henrique de
Paula Alvarenga
Federal University
of Technology  Paraná (UTFPR), Brazil
Email: thpalvarenga@hotmail.com
Ademir José de
Abreu
Instituto de Ensino
Superior Presidente Tancredo de Almeida Neves, Brazil
Email: ademirjabreu@hotmail.com
Cassiano Moro
Piekarski
Federal University
of Technology  Paraná (UTFPR), Brazil
Email: cassianopiekarski@gmail.com
Juliana Vitória
Messias Bittencourt
Federal University
of Technology  Paraná (UTFPR), Brazil
Email: julianavitoria@utfpr.edu.br
Eloiza Aparecida
Silva Ávila de Matos
Federal University
of Technology  Paraná (UTFPR), Brazil
Email: elomatos@utfpr.edu.br
Submission:
21/09/2013
Accept:
05/10/2013
ABSTRACT
By reason of the requirements of quality on the part of consumers and
regulatory agencies, the dairy industries require tools capable of optimizing
their processes in virtue of threats from countries which have a lower cost of
production. The Statistical Process Control (SPC) is a powerful tool to
evaluate and monitor the process in relation to their stability. This paper
presents an application of Statistical Process Control (SPC) in a dairy plant
located in the south of Minas Gerais. The process analyzed was the packaging of
butter in 200g pots. The purpose of this article is to identify the actual
state of the filling process of butter in this dairy and compare them with the
requirements established by legislation. Therefore, was used samples and
control charts to demonstrate the current state of the process and normality
tests, in particular the tstudent. The results demonstrate that the industry
does not harm the consumer and that is faithful to the legislation. However, it
was identified that in case the industry presents an overweight in nominal
content of each package, which leads to considerable injury once the feedstock
used in the production of butter (cream) is of great economic value.
Keywords: Statistical
process control; control charts; dairy.
1. INTRODUCTION
Milk
production and its derivatives play an important role on the national stage,
whether in economics, is the social aspect as employment generation,
maintenance of the population in rural areas and improving the quality of life
in rural areas (CAPUCHO; PARRÉ, 2012).
The
importance of this industry can be seen in the context of agribusiness, where
it is referred to as one of the leading sectors in terms of national income and
tax revenues (SOUZA, 2006). O leite e seus derivados estão entre os seis
primeiros produtos mais importantes da agropecuária nacional, ficando à frente
de produtos de culturas tradicionais como café e o arroz. Para cada real
acrescido na produção no sistema agroindustrial do leite, há um crescimento de,
aproximadamente, cinco reais no aumento do Produto Interno Bruto – PIB, o que
coloca o agronegócio do leite à frente de setores importantes como o da
siderurgia e o da indústria têxtil (EMBRAPA, 2003).
However,
the domestic market is being threatened by products from the countries of the
Southern Common Market (MERCOSUR) in terms of its low production cost. Thus,
the competitiveness and survival of dairy products are linked to a national
quality management. By this fact, the main determinants for longevity of dairy
is a national quality management based on reducing costs and waste, since most
of the population still considers the price as a major factor in the purchase
decision (SCALCO; TOLEDO, 2002). The end of the pricefixing of milk in 1991
and the economic opening of the country exposed the weaknesses and deficiencies
in organization and technology in the dairy sector national (WINCLER; SANTOS;
MACHADO, 2013).
For
industries, one of the key to success is to stabilize their processes ensuring
product reliability by reducing waste. An accepted definition of quality is to
reduce the variability that the smaller, the better the reliability and
acceptance of the product or service. To reduce variability tools Statistical
Process Control (SPC) to demonstrate efficient stabilization of production
processes (KHEDIRI; WEIHS; LIMAM, 2010; MILAN; FERNANDES, 2002).
The
Statistical Process Control (SPC) is a set of statistical tools for quality
oriented problem solving environment in processes and decision making by managers.
The CEP seeks accuracy in manufacturing, using data to analyze the process. In
the CEP process prevents loss (waste) products through control limits
(CHAKRABORTY; TAH, 2006; DINIZ, 2001). It is quite simple being used in various
industries worldwide. Through it, it is possible to control important features
of the product and the process instantly, ensuring quality levels at an
affordable cost. The SPC uses statistics to analyze the limitations of the
product and process (NOMELINI; FERREIRA; OLIVEIRA, 2009; SINGH; GILBREATH,
2002).
The
SPC is composed of seven major tools, which were understood by histograms,
check sheets, Pareto charts, causeeffect diagrams, diagrams concentration
defect (stratification), scatter diagrams, and control charts (Vieira, 1999).
Among the tools SPC control charts are one of the most popular tools. These
graphics can be based on attributes, or variables (SOUZA; RIGÃO, 2005).
A
control chart is composed of three parallel lines, one central represents the
average value (CL), the lower representing the lower control limit (LCL) and
upper one representing the upper control limit (UCL). Are presented on points
representing the samples taken at various times of the process (DINIZ, 2001;
VIEIRA, 1999).
The
control process is performed by measuring the variables in separate points in
control charts. During the measurements, the results are checked against the
control limits which are expected according to the desired pattern. The results
obtained from the measurements indicates that the process has random or
specific causes of variability (KHEDIRI; WEIHS; LIMAM, 2010; PAESE; CATEN;
RIBEIRO, 2001).
So
that the process is under control it is necessary that your points are within
the control limits and your presentation is random at the top and bottom of the
middle line representing the quality characteristic (VIEIRA, 1999; DINIZ, 2001;
CARVALHO, 2008). The measurements show that outside the control limits of
variability are considered special, i.e. affecting the quality of the product.
Upon detecting such causes of variation can act on the process to improve the
quality of the product continuously (CARVALHO, 2008; DINIZ, 2001; MICHEL;
FOGLIATTO, 2002; RAMOS, 2000; VIEIRA, 1999).
Although
the agrifood sector present an unquestionable relevance to Brazil, is only seen
a small amount of research surrounding the issue of quality management in the
sector (TOLEDO; BATALHA; AMARAL, 2000). Given the above, this paper aims to
apply Statistical Process Control (SPC) in the process of filling of butter in
a Cooperative Dairy located in Lavras in southern Minas Gerais and check if
this process has stability and content 200g pots of butter is within the
standards of the National Institute of Metrology and Industrial Quality
(INMETRO).
2. MATERIAL AND METHODS
The
study was conducted under a Cooperative Dairy Lavras located in the south of
Minas Gerais. The Statistical Process Control (SPC) was applied in the process
of filling of butter in 200g pots in order to verify that the products are
under statistical control and meet specifications INMETRO No. 248, July 17,
2008. To obtain the weights of the pots of butter (finished product), they were
weighed on the same plant by using two scales Gehaka  semianalytical model
BK300, with a maximum capacity of 310g, as recorded in INMETRO INMETRO seal
188 / 2003. The two scales showed no significant difference in the values
acquired through weighing, only differences being observed in the third house
after of the point.
The
data analyzed correspond to eight productions (batches) of butter in 200g pots
 between the months of May and August of 2011. To carry out all the procedures
for applying the SPC (applying the Student t test and Wilcoxon test) was used
Rsoftware, as well as their respective libraries for each proposed analysis
thus were made use of packages: library (qcc); require (gdata); library (BSDA)
and function t test. Through the Rsoftware, were generated consolidated
statistics as the histogram, control charts for variables and the t test. The conventions
used in control charts were described as upper specification limit and lower
specification limit, which match the criteria defined by INMETRO in the
ordinance in question. The lower and upper control limits of the statistical
analysis are determined in accordance with the process variability purchased in
batches surveyed.
The
National Institute of Metrology, Standardization and Industrial Quality
(INMETRO) regularly conducts tests concerning the veracity of a product in
relation to its weight, volume and diameter. Such tests are reported in the
media and the credibility of the industries analyzed is put to the test with
such disclosure. It is a federal agency under the Ministry of Development,
Industry and Foreign Trade, whose mission is to provide confidence to the
Brazilian society in the measurements and products through metrology and
conformity assessment, promoting the harmonization of consumer relations,
innovation and the country's competitiveness (INMETRO, 2011).
The
butter milk derivative is produced and marketed in weight (grams and kilogram)
without the presence of the consumer. In this respect, INMETRO No. 248, July
17, 2008 aims to establish criteria for checking the actual content of
premeasured products with nominal content (Qn) equal, expressed in units of
the International System of Units. This Ordinance applies to the metrological
control of premeasured products in manufacturing environments, deposits and
retail outlets.
According
to INMETRO No. 248, July 17, 2008, Product PreMeasured content rating equal is
defined as any packaged product and / or measured without the presence of the
consumer, with equal and predetermined nominal content in packaging during
manufacturing. In the production process it is clear that there are variability’s.
At this point, the said Ordinance establishes individual tolerances for
checking the weight / volume of the product in relation to its liquidity. Table
1 provides acceptable tolerance by the standard:
Table 1:
Tolerances for individual allowable mass and volume

INDIVIDUAL
TOLERANCE (T) 

Nominal content (Qn) grams or millgrams 5 to 50 50 to 100 100 to 200 200 to 300 300 to 500 500 to 1000 1000 to 10000 10000 to 15000 15000 to 25000 
Percentage (%) of Qn 9  4,5  3  1,5  1 
grams or millgrams  4,5  9  15  150  

Source:
INMETRO (2008)
Since
pots of butter (pots) are 200g obeys individual tolerance 9g contained in Table
1. The INMETRO No. 248, July 17, 2008, this content is already subtracted the
average weight of packaging, in this context, this individual tolerance it is
only the product.
However,
INMETRO No. 248, July 17, 2008, also provides for batches produced the quantity
of items to be sampled and the amount of items containing liquid below the
individual tolerance contained in Table 1. Table 2 presents the sample to the
control and maximum number of defective items:
Table 2: Sample
for control and maximum number of defective items
Batch Size 
Sample
Size 
Criteria
for acceptance average 
Maximum defective below QnT 

9 to 25 26 to 50 51 to 149 150 to 4000 4001 to 10000 
5 13 20 32 80 
X ≥ Qn – 2.059 x S X ≥ Qn – 0.847 x S X ≥ Qn – 0.640 x S X ≥ Qn – 0.485 x S X ≥ Qn – 0.295 x S 
0 1 1 2 5 

Source:
INMETRO (2008)
Regarding
Table 2, to accept the corresponding average of the sample as mean (X), must be
greater or equal to the nominal capacity (Qn), unless the tabular values
contained in the table for each sample size, multiplied by the deviation
standard (S) of the samples collected.
3. RESULTS
The
samples were arranged according to the eight batches sampled between May and
August 2011, which are presented in Table 3 arranged in eight (08) samples,
divided into rational subgroups with n = 32:
The
sample size was set at n = 32, according to INMETRO No. 248, July 17, 2008, for
the production of dairy fits the average of 1,000 pots of butter per batch.
Therefore, it was determined that the jump from one sample to another 31 was
produced items, i.e. items produced every 31 withdrawing a sample and so forth.
In
the literature (DINIZ, 2000; MONTGOMERY, 2009; RAMOS, 1999), is very easily to
control charts for variables to have answers expressed by a number on a scale
discrete measures. Thus, in Table 4, shows the limits of the control charts as
well as the main equations adopted in this work:
Table 3: Samples
collected in the period from May to August/2011
Sample 1 
Sample 2 
Sample 3 
Sample 4 
Sample 5 
Sample 6 
Sample 7 
Sample 8 
202.4 
201.4 
199.3 
203.0 
201.9 
203.2 
202.6 
201.1 
205.8 
209.5 
208.8 
205.6 
205.7 
207.4 
204.2 
204.2 
205.1 
208.3 
209.3 
203.2 
204.5 
207.6 
207.7 
203.1 
205.5 
209.5 
209.3 
203.9 
208.2 
209.3 
208.4 
204.0 
206.6 
216.0 
206.0 
202.8 
210.1 
209.1 
209.6 
207.3 
205.3 
211.0 
207.6 
205.7 
210.6 
208.5 
210.2 
207.7 
206.4 
208.7 
208.4 
204.5 
209.6 
208.6 
208.9 
207.8 
207.6 
209.7 
210.2 
207.5 
209.4 
210.5 
211.5 
208.3 
204.4 
207.2 
209.1 
208.9 
209.7 
209.2 
212.3 
210.6 
205.4 
207.1 
206.2 
208.0 
210.2 
208.5 
211.2 
210.4 
206.1 
208.3 
206.4 
210.7 
210.6 
210.7 
210.3 
208.2 
206.6 
208.0 
206.2 
207.7 
210.5 
211.0 
209.0 
208.5 
206.1 
208.1 
207.1 
211.7 
212.6 
209.3 
211.6 
209.5 
206.7 
207.9 
208.7 
214.5 
211.3 
208.4 
211.8 
210.3 
206.8 
206.8 
208.9 
212.9 
211.1 
211.2 
210.4 
211.7 
206.9 
207.7 
203.9 
213.5 
209.1 
210.1 
209.2 
210.6 
206.6 
208.2 
206.2 
209.4 
208.5 
208.4 
210.1 
211.0 
206.1 
206.9 
205.8 
210.5 
209.5 
208.5 
209.2 
212.4 
216.0 
207.3 
206.6 
209.9 
211.1 
210.2 
211.5 
211.1 
210.5 
208.9 
206.7 
208.6 
210.0 
211.8 
209.8 
211.9 
215.7 
207.7 
206.9 
207.7 
208.9 
210.7 
212.4 
210.2 
210.6 
210.7 
206.9 
208.5 
211.6 
209.4 
210.1 
208.6 
216.1 
208.7 
207.5 
208.3 
207.8 
211.7 
211.3 
210.6 
206.2 
209.9 
210.4 
209.5 
211.6 
208.5 
209.1 
212.3 
215.2 
209.1 
207.9 
206.3 
213.5 
209.4 
211.5 
210.3 
203.1 
210.2 
208.6 
208.7 
211.6 
210.7 
212.2 
208.2 
214.1 
210.4 
207.1 
210.2 
208.5 
208.9 
211.3 
212.8 
213.1 
216.2 
207.5 
211.3 
210.6 
208.4 
210.7 
210.2 
203.8 
209.2 
207.8 
212.6 
210.7 
211.0 
211.4 
212.1 
203.8 
206.8 
207.3 
209.5 
214.4 
212.6 
212.5 
210.4 
213.9 
211.0 
209.2 
208.4 
208.2 
210.6 
211.4 
211.3 
213.0 
208.1 
207.3 
207.6 
209.4 
209.0 
212.5 
210.6 
Source: Survey data
To
prove that the average weight of butter jars fit the average interval specified
by ordinance, formulated two hypotheses, where (average limits are equal); and, (average limits are different). In this
respect, Ferreira (2009) describes a good test for this type of comparison is
the average student t test. Therefore, reject in favor of at a significance level of 5%, in other words,
the average interval specified is 191g and 209g, while the average interval was
found in the sample of 208.60g and 209.29g. The Table 5 shows the results of
the comparisons = 200g and the average sample:
Table 4: Limits
of graphs and equations adopted in the research

Mean and standard deviation 
Mean and standard deviation unknown 

_{} 
_{} 
_{} e LCL 
_{} 
_{} 
Formulas adopted in
line with INMETRO 248/2008 

Average 
_{} 
_{ } _{} is the average of the sampled values _{}
is the observed value of each point _{} is the sample size

Deviation 
_{} 
_{} is the average of the sampled values _{}
is the observed value of each point _{}
is the standard deviation of the sample _{} is the sample size 
Jump 
_{} 
_{}
the jump is performed for each sample _{} is the lot size produced _{} is the sample size

Source:
Authors
Table
5. Results of comparisons between _{} = 200g and the average sample
Item 
LCL 
CL 
UCL 
pvalue 
Assurance 
Global 
208.60 
208.94 
209.29 
2.20E16 
95% 
Sample 1 (Y1) 
206.66 
208.17 
209.67 
2.67E09 
95% 
Sample 2 (Y2) 
207.96 
208.89 
209.82 
2.20E16 
95% 
Sample 3 (Y3) 
206.61 
207.35 
208.09 
2.20E16 
95% 
Sample 4 (Y4) 
207.39 
208.49 
209.58 
2.20E16 
95% 
Sample 5 (Y5) 
208.86 
209.73 
210.61 
2.20E16 
95% 
Sample 6 (Y6) 
208.83 
209.45 
210.07 
2.20E16 
95% 
Sample 7 (Y7) 
209.39 
210.18 
210.98 
2.20E16 
95% 
Sample 8 (Y8) 
208.27 
209.29 
210.31 
2.20E16 
95% 
Source: Survey data
It is
clarified that the test was applied globally (all elements of the sample) and
then to the sample group only as a precaution, in order to verify if any sample
would cause variation between them. Note that the test was significant at 95%
confidence level with pvalue greater than 16th after of the point.
Figure
1 shows the control charts generated by R software with sample data, organized
as follows: R Chart  Graph control amplitude; S Chart  Graph Control Standard
Deviation; xbar Chart (left)  Graph
Control Average of the natural limits of the process; xbar Chart (right) 
Average Control graph with the limits INMETRO.
Figure
1: Graphs of the research generated by the software R
Source: Survey data
A
distribution cannot be defined solely by their average, requiring a knowledge
of dispersion around the sample mean. This knowledge can be acquired through
the graph of the standard deviation or the graph of amplitude (DINIZ, 2001).
The values of the samples in Chart 1 (amplitude) had
low variability, and only one sample (sample 5) was presented outside the control
limits. In Chart 2 (standard deviation) all samples were stable, with all the
elements contained within the lower and upper control.
Charts
3 and 4 show the natural limits of the samples (Chart 3) and the specification
limits (Chart 4). Note that in both graphs for redflagged samples, whose
significance is the lack of stability. According to Montgomery (2009),
processes that have special causes of variation are called out of statistical
control, since they are responsible for the increase in manufacturing costs.
The same author also states that the stability of a process cannot be measured
only by the fact that the points are within the control limits. He argues that
there are cases in which the existence of more than 7 points between sequential
mean and limits, sets up lack of stability.
The
ability of a process can be understood as the natural variability of item
regarding their specifications. Thus, the ability to identify a process, it is
necessary to use capability indices, the most used and Cp index Cpk. Figure 2
shows two graphs of process capability of the dairy:
Figure 2: Graphs
of capacity generated by the software R
Source:
Survey data
The
index Cp is defined by Ramos (2000) as being the ratio between the total
dispersion and engineering tolerate the procedure. The same authors also
described that this index compares the total variation allowed by specification
with the dispersion consumed by the process. If Cp1, this
indicates that the process is capable of achieving the specification. Already
another index (Cpk) is also defined by the same author as the average distance
evaluation process regarding the specification limits, taking into account that
it is lower, i.e. more critical. If Cpk1, then the
process is capable. Montgomery (2004) argues that Cp analyzes the potential
capacity of the process, while Cpk analyzes the effective capacity.
Note
in the chart 1 of Figure 2, both the Cp value as the Cpk is > 1, the two
indices of 1.23. Already chart 2 of the same figure shows the index Cp with the
same 1.23 and Cpk index of 0.0078. This difference between the indices Cpk
charts, occurs because of the first to be generated by the natural limits of
the process and the second by the specification limits. The process analyzed as
shown in Figure 3, shows low variability in their control limits with a
standard deviation of 2.43; however is outside the limits specified by
ordinance mentioned.
4. CONCLUSIONS
The
implementation of the SPC in the filling dairy process identified instability
and even still possible to know the number of grams in losses filling product
(butter) excess in 200g pots.
The
dairy analyzed satisfactorily meets the minimum specifications of INMETRO No.
248, July 17, 2008, which establishes a lower control limit of 191g and an
average weight of 200g. However, it is observed that the average interval of
the weights is not centered in 200g, according to the results of the tests:
Student t and Wilcoxon. The true average is centered on 208.94 g with 95% confidence.
Thus, it appears that the company is sending over 4.47% of output per batch
equivalent to 8,943g.
It is
observed that on the product weight must be corrected in order to reduce
operating costs of the company, since 45 pots (8.943g) of butter are lost
production (batch). The process has low variability, but it is mostly above the
upper specification limit. For this purpose, it is recommended to realign the
process, maintaining low rates of change, so that it does not cause damage to
the company which results in considerable loss since the raw material used in
the production of butter (cream) is great economic value in the dairy industry.
REFERENCES
CAPUCHO,
T. O.; PARRÉ, J. L. (2012) Milk production in Paraná: a study considering the
spatial effects. Informe GEPEC Journal. v. 16, n: 1, p. 112127.
CARVALHO, M. M.; (2008)
Qualidade. In: BATALHA, M. O. Introdução
à engenharia da produção. Rio de Janeiro: Elsevier. cap. 4, p. 5377.
CHAKRABORTY,
S.; TAH, D. (2006) Real time statistical process advisor for effective quality
control. Decision Support Systems. v. 42, p. 700711.
DINIZ, M. G. (2001) Desmistificando o controle estatístico de
processo. São Paulo: Artliber.
EMBRAPA. (2003) Empresa Brasileira de Agropecuária.
Embrapa  Gado de leite. Sistema de Produção de Leite (Zona da Mata Atlântica),
jan. 2003. Disponível em: <
http://sistemasdeproducao.cnptia.embrapa.br/FontesHTML/Leite/LeiteZonadaMataAtlantica/index.htm > Acesso: 21 ago. 2012.
FERREIRA, D. F. (2009) Estatística básica. Lavras: UFLA.
INMETRO (2008)  INSTITUTO NACIONAL DE METROLOGIA,
NORMALIZAÇÃO E QUALIDADE INDUSTRIAL. Portaria INMETRO N° 248, de 17 de
julho de 2008.
KHEDIRI,
I. B.; WEIHS, C.; LIMAM, M. (2010) Support Vector Regression control charts for
multivariate nonlinear autocorrelated processes. Chemometrics and Intelligent Laboratory Systems. v. 103, p. 76–81.
MILAN,
M.; FERNANDES, R. A. T. (2002) Quality of tillage operations by statistical
process control. Scientia
Agricola. v.59, n:2, p. 261266,
abr/jun.
MONTGOMERY, D. C. (2009) Introdução ao controle estatístico de
qualidade. Rio de Janeiro: LTC.
NOMELINI, Q. S. S.; FERREIRA, E.
B.; OLIVEIRA, M. A. (2009) Studies on nonrandom patterns in Shewhart control
charts. Gestão & Produção (UFSCar). v:
16, n: 3, p. 414421.
PAESE, C.; CATEN, C. T.;
RIBEIRO, J. L. D. (2001) Aplicação da análise de variância na implantação do
CEP. Produção. v.
11, n. 1, p. 1726, nov.
R
DEVELOPMENT Core Team. (2009) A language and environment for statistical
computing. Foundation for Statistical
Computing, Vienna,
Austria. Disponível em: < http://www.Rproject.org > Acesso em: 21 out.
2010.
RAMOS, A. W. (2000) CEP para processos contínuos e em
bateladas. São Paulo. Edgard Blücher.
SCALCO, A. R.; TOLEDO, J. C.
(2002) Gestão da qualidade em laticínios do estado de São Paulo: situação atual
e recomendações. RAUSP.
v. 37, n. 2, p. 1725, abr/jun.
SINGHA,
R.; GILBREATHB, G. (2002) A realtime information system for multivariate
statistical process control. International
Journal Production Economics. v. 75, p.161–172.
SOUZA, A. F. C. (2006) Utilização de técnicas de análise
multivariada para identificação do perfil dos laticínios de micro e pequeno
porte do Estado de Minas Gerais. 2006. 96f. Dissertação (Mestrado em
Ciência e Tecnologia de Alimentos) Universidade Federal de Viçosa. Viçosa.
SOUZA, A. M.; RIGÃO, M. H.
(2005) Identificação de variáveis fora de controle em processos produtivos
multivariados. Produção. v. 15, n.
1, p. 7486, jan/abr.
TOLEDO, J. C.; BATALHA, M. O.;
AMARAL, D. C. (2000) Qualidade na indústria agroalimentar: situação atual e
perspectivas. Revista de Administração
de Empresas (FGV). São Paulo. v. 40, n. 2, p. 90101, abr/jun.
VIERIA, S. (1999) Estatística para a qualidade: como avaliar
com precisão a qualidade em produtos e serviços. Rio de Janeiro:
Elsevier.
WINCKLER,
N. C.; SANTOS, T. S.; MACHADO, J. A. D. (2013) Coopetition between household
farmers of milk production chain in west of Santa. Revista Brasileira
de Gestão e Desenvolvimento Regional. v. 9, n. 1, p. 4066, jan/mar.
Article Metrics
_{Metrics powered by PLOS ALM}
Refbacks
 There are currently no refbacks.
Copyright (c)
LIBRARIES BY  